36 citations · 36 across the 8 of their papers we have counts for
10 papers
The curse of dimensionality for geometric -discrepancies with nonnegative weights
Josef Dick
We prove that the normalized star, extreme, and periodic -discrepancies with arbitrary nonnegative weights suffer from the curse of dimensionality. A single elementary lemma i…
Spherical Cap Discrepancy -- Blessing of Dimensionality and a Balanced Large-Cap Variant
Johann S. Brauchart, Josef Dick, Friedrich Pillichshammer
We prove that the information complexity (i.e., the inverse) of the classical spherical cap discrepancy on the -dimensional sphere decreases with dimension…
Worst-case -approximation of periodic functions using median lattice algorithms
Zexin Pan, Mou Cai, Josef Dick +2
We study the worst-case approximation of multivariate periodic functions from the weighted Korobov space with smoothness in the Lebesgue norm for…
The inverse of the star discrepancy of a union of randomly shifted Korobov rank-1 lattice point sets depends polynomially on the dimension
Jiarui Du, Josef Dick
The inverse of the star discrepancy, , defined as the minimum number of points required to achieve a star discrepancy of at most in dimension , is known to depend l…
A lattice algorithm with multiple shifts for function approximation in Korobov spaces
Mou Cai, Josef Dick, Takashi Goda
In this paper, we propose a novel algorithm for function approximation in a weighted Korobov space based on shifted rank-1 lattice rules. To mitigate aliasing errors inherent in la…
On the quasi-uniformity properties of quasi-Monte Carlo point sets and sequences -- Part I: Lattices and Kronecker sequences
Josef Dick, Takashi Goda, Gerhard Larcher +2
The discrepancy of a point set quantifies how well the points are distributed, with low-discrepancy point sets demonstrating exceptional uniform distribution properties. Such sets…
On the quasi-uniformity properties of quasi-Monte Carlo point sets and sequences -- Part II: digital nets and sequences
Josef Dick, Takashi Goda, Kosuke Suzuki
We study the quasi-uniformity properties of digital nets, a class of quasi-Monte Carlo point sets. Quasi-uniformity is a space-filling property used for instance in experimental de…
Tractability results for integration in subspaces of the Wiener algebra
Josef Dick, Takashi Goda, Kosuke Suzuki
In this paper, we present some new (in-)tractability results related to the integration problem in subspaces of the Wiener algebra over the -dimensional unit cube. We show that…
A Discrepancy Bound for Deterministic Acceptance-Rejection Samplers Beyond in Dimension 1
Houying Zhu, Josef Dick
In this paper we consider an acceptance-rejection (AR) sampler based on deterministic driver sequences. We prove that the discrepancy of an element sample set generated in this…
Point sets on the sphere with small spherical cap discrepancy
Christoph Aistleitner, Johann Brauchart, Josef Dick
In this paper we study the geometric discrepancy of explicit constructions of uniformly distributed points on the two-dimensional unit sphere. We show that the spherical cap discre…